Showing papers on "Operator (computer programming) published in 2012"

Operator product expansion convergence in conformal field theory

Abstract: We clarify questions related to the convergence of the operator product expansion and conformal block decomposition in unitary conformal field theories (for any number of spacetime dimensions). In particular, we explain why these expansions are convergent in a finite region. We also show that the convergence is exponentially fast, in the sense that the operators of dimension above Delta contribute to correlation functions at most exp(-a Delta). Here the constant a > 0 depends on the positions of operator insertions and we compute it explicitly.

Code symbol reading system supporting operator-dependent system configuration parameters

Abstract: A method of and system for setting and switching user preferences between system operators, to provide a higher return on investment (ROI) and a more satisfying work environment. The system allows operators to easily select and implement particular customizable system configuration parameters (SCPs) in a code symbol reading system, based on personal preferences of the system operator, which can lead to more effective scanning performance. A different set of customizable SCPs are programmably stored in system memory (e.g. EPROM) for each system operator/user registered to use the system, to improve the quality of the working environment and increase worker productivity.

Intuitionistic Fuzzy Information Aggregation Using Einstein Operations

Abstract: Aggregation of fuzzy information is a new branch of Atanassov's intuitionistic fuzzy set (AIFS) theory, which has attracted significant interest from researchers in recent years. In this paper, we treat the intuitionistic fuzzy aggregation operators with the help of Einstein operations. We first introduce some new operations of AIFSs, such as Einstein sum, Einstein product, and Einstein scalar multiplication. Then, we develop some intuitionistic fuzzy aggregation operators, such as the intuitionistic fuzzy Einstein weighted averaging operator and the intuitionistic fuzzy Einstein ordered weighted averaging operator, which extend the weighted averaging operator and the ordered weighted averaging operator to aggregate Atanassov's intuitionistic fuzzy values, respectively. We further establish various properties of these operators and analyze the relations between these operators and the existing intuitionistic fuzzy aggregation operators. Moreover, we give some numerical examples to illustrate the developed aggregation operators. Finally, we apply the intuitionistic fuzzy Einstein weighted averaging operator to multiple attribute decision making with intuitionistic fuzzy information.

The Bootstrap Program for Boundary CFT_d

Abstract: We study the constraints of crossing symmetry and unitarity for conformal field theories in the presence of a boundary, with a focus on the Ising model in various dimensions. We show that an analytic approach to the bootstrap is feasible for free-field theory and at one loop in the epsilon expansion, but more generally one has to resort to numerical methods. Using the recently developed linear programming techniques we find several interesting bounds for operator dimensions and OPE coefficients and comment on their physical relevance. We also show that the "boundary bootstrap" can be easily applied to correlation functions of tensorial operators and study the stress tensor as an example. In the appendices we present conformal block decompositions of a variety of physically interesting correlation functions.

Effective operator formalism for open quantum systems

Abstract: We present an effective operator formalism for open quantum systems. Employing perturbation theory and adiabatic elimination of excited states for a weakly driven system, we derive an effective master equation which reduces the evolution to the ground-state dynamics. The effective evolution involves a single effective Hamiltonian and one effective Lindblad operator for each naturally occurring decay process. Simple expressions are derived for the effective operators which can be directly applied to reach effective equations of motion for the ground states. We compare our method with the hitherto existing concepts for effective interactions and present physical examples for the application of our formalism, including dissipative state preparation by engineered decay processes.

Systems of dyadic cubes in a doubling metric space

Abstract: A number of recent results in Euclidean Harmonic Analysis have exploited several adjacent systems of dyadic cubes, instead of just one fixed system. In this paper, we extend such constructions to general spaces of homogeneous type, making these tools available for Analysis on metric spaces. The results include a new (non-random) construction of boundedly many adjacent dyadic systems with useful covering properties, and a streamlined version of the random construction recently devised by H. Martikainen and the first author. We illustrate the usefulness of these constructions with applications to weighted inequalities and the BMO space; further applications will appear in forthcoming work.

Reduced Basis Approximation for Nonlinear Parametrized Evolution Equations based on Empirical Operator Interpolation

Abstract: We present a new approach to treating nonlinear operators in reduced basis approximations of parametrized evolution equations. Our approach is based on empirical interpolation of nonlinear differential operators and their Frechet derivatives. Efficient offline/online decomposition is obtained for discrete operators that allow an efficient evaluation for a certain set of interpolation functionals. An a posteriori error estimate for the resulting reduced basis method is derived and analyzed numerically. We introduce a new algorithm, the PODEI-greedy algorithm, which constructs the reduced basis spaces for the empirical interpolation and for the numerical scheme in a synchronized way. The approach is applied to nonlinear parabolic and hyperbolic equations based on explicit or implicit finite volume discretizations. We show that the resulting reduced scheme is able to capture the evolution of both smooth and discontinuous solutions. In case of symmetries of the problem, the approach realizes an automatic and intuitive space-compression or even space-dimensionality reduction. We perform empirical investigations of the error convergence and run-times. In all cases we obtain a good run-time acceleration.

Effective theories of single field inflation when heavy fields matter

Abstract: We compute the low energy effective field theory (EFT) expansion for single-field inflationary models that descend from a parent theory containing multiple other scalar fields. By assuming that all other degrees of freedom in the parent theory are sufficiently massive relative to the inflaton, it is possible to derive an EFT valid to arbitrary order in perturbations, provided certain generalized adiabaticity conditions are respected. These conditions permit a consistent low energy EFT description even when the inflaton deviates off its adiabatic minimum along its slowly rolling trajectory. By generalizing the formalism that identifies the adiabatic mode with the Goldstone boson of this spontaneously broken time translational symmetry prior to the integration of the heavy fields, we show that this invariance of the parent theory dictates the entire non-perturbative structure of the descendent EFT. The couplings of this theory can be written entirely in terms of the reduced speed of sound of adiabatic perturbations. The resulting operator expansion is distinguishable from that of other scenarios, such as standard single inflation or DBI inflation. In particular, we re-derive how certain operators can become transiently strongly coupled along the inflaton trajectory, consistent with slow-roll and the validity of the EFT expansion, imprinting features in the primordial power spectrum, and we deduce the relevant cubic operators that imply distinct signatures in the primordial bispectrum which may soon be constrained by observations. We dedicate this paper to the memory of our dear colleague and friend, Sjoerd Hardeman. His ideas, insights and diligence permeates every aspect of this work.

Privacy-Preserving Stream Aggregation with Fault Tolerance

Abstract: We consider applications where an untrusted aggregator would like to collect privacy sensitive data from users, and compute aggregate statistics periodically. For example, imagine a smart grid operator who wishes to aggregate the total power consumption of a neighborhood every ten minutes; or a market researcher who wishes to track the fraction of population watching ESPN on an hourly basis.

Interval-valued intuitionistic fuzzy prioritized operators and their application in group decision making

Abstract: This study investigates the group decision making under interval-valued intuitionistic fuzzy environment in which the attributes and experts are in different priority level. We first propose some interval-valued intuitionistic fuzzy aggregation operators such as the interval-valued intuitionistic fuzzy prioritized weighted average (IVIFPWA) operator, the interval-valued intuitionistic fuzzy prioritized weighted geometric (IVIFPWG) operator. These proposed operators can capture the prioritization phenomenon among the aggregated arguments. Then, some of their desirable properties are investigated in detail. Furthermore, an approach to multi-criteria group decision making based on the proposed operators is given under interval-valued intuitionistic fuzzy environment. Finally, a practical example about talent introduction is provided to illustrate the developed method.

Nonlinear Diffusion with Fractional Laplacian Operators

Abstract: We describe two models of flow in porous media including nonlocal (long-range) diffusion effects. The first model is based on Darcy’s law and the pressure is related to the density by an inverse fractional Laplacian operator. We prove existence of solutions that propagate with finite speed. The model has the very interesting property that mass preserving self-similar solutions can be found by solving an elliptic obstacle problem with fractional Laplacian for the pair pressure-density. We use entropy methods to show that these special solutions describe the asymptotic behavior of a wide class of solutions.

Fit and diverse: set evolution for inspiring 3D shape galleries

Abstract: We introduce set evolution as a means for creative 3D shape modeling, where an initial population of 3D models is evolved to produce generations of novel shapes. Part of the evolving set is presented to a user as a shape gallery to offer modeling suggestions. User preferences define the fitness for the evolution so that over time, the shape population will mainly consist of individuals with good fitness. However, to inspire the user's creativity, we must also keep the evolving set diverse. Hence the evolution is "fit and diverse", drawing motivation from evolution theory. We introduce a novel part crossover operator which works at the finer-level part structures of the shapes, leading to significant variations and thus increased diversity in the evolved shape structures. Diversity is also achieved by explicitly compromising the fitness scores on a portion of the evolving population. We demonstrate the effectiveness of set evolution on man-made shapes. We show that selecting only models with high fitness leads to an elite population with low diversity. By keeping the population fit and diverse, the evolution can generate inspiring, and sometimes unexpected, shapes.

Improved bounds for CFT's with global symmetries

Abstract: The four point functions of Conformal Field Theories (CFT’s) with global symmetries give rise to multiple crossing symmetry constraints. We explicitly study the correlator of four scalar operators transforming in the fundamental representation of a global SO(N) and the correlator of chiral and anti-chiral superfields in a superconformal field theory. In both cases the constraints take the form of a triple sum rule, whose feasibility can be translated into restrictions on the CFT spectrum and interactions. In the case of SO(N) global symmetry we derive bounds for the first scalar singlet operator entering the Operator Product Expansion (OPE) of two fundamental representations for different value of N. Bounds for the first scalar traceless-symmetric representation of the global symmetry are computed as well. Results for superconformal field theories improve previous investigations due to the use of the full set of constraints. Our analysis only assumes unitarity of the CFT, crossing symmetry of the four point function and existence of an OPE for scalars.

Surface operators in {N} = 2 4d gauge theories

Abstract: $ \mathcal{N} $ = 2 four dimensional gauge theories admit interesting half BPS surface operators preserving a (2, 2) two dimensional SUSY algebra. Typical examples are (2, 2) 2d sigma models with a flavor symmetry which is coupled to the 4d gauge fields. Interesting features of such 2d sigma models, such as (twisted) chiral rings, and the tt* geometry, can be carried over to the surface operators, and are affected in surprising ways by the coupling to 4d degrees of freedom. We describe in detail a relation between the parameter space of twisted couplings of the surface operator and the Seiberg-Witten geometry of the bulk theory. We discuss a similar result about the tt* geometry of the surface operator. We predict the existence and general features of a wall-crossing formula for BPS particles bound to the surface operator.

Full linearized Fokker–Planck collisions in neoclassical transport simulations

Abstract: The complete linearized Fokker–Planck collision operator has been implemented in the drift-kinetic code NEO (Belli and Candy 2008 Plasma Phys. Control. Fusion 50 095010) for the calculation of neoclassical transport coefficients and flows. A key aspect of this work is the development of a fast numerical algorithm for treatment of the field particle operator. This Eulerian algorithm can accurately treat the disparate velocity scales that arise in the case of multi-species plasmas. Specifically, a Legendre series expansion in ξ (the cosine of the pitch angle) is combined with a novel Laguerre spectral method in energy to ameliorate the rapid numerical precision loss that occurs for traditional Laguerre spectral methods. We demonstrate the superiority of this approach to alternative spectral and finite-element schemes. The physical accuracy and limitations of more commonly used model collision operators, such as the Connor and Hirshman–Sigmar operators, are studied, and the effects on neoclassical impurity poloidal flows and neoclassical transport for experimental parameters are explored.

Some dependent aggregation operators with 2-tuple linguistic information and their application to multiple attribute group decision making

Abstract: We investigate the multiple attribute group decision making (MAGDM) problems in which the attribute values take the form of 2-tuple linguistic information. Motivated by the ideal of dependent aggregation [Xu, Z. S. (2006). Dependent OWA operators. Lecture Notes in Artificial Intelligence, 3885, 172-178], in this paper, we develop some dependent 2-tuple linguistic aggregation operators: the dependent 2-tuple ordered weighted averaging (D2TOWA) operator and the dependent 2-tuple ordered weighted geometric (D2TOWG) operator, in which the associated weights only depend on the aggregated 2-tuple linguistic arguments and can relieve the influence of unfair 2-tuple linguistic arguments on the aggregated results by assigning low weights to those ''false'' and ''biased'' ones and then apply them to develop some approaches for multiple attribute group decision making with 2-tuples linguistic information. Finally, some illustrative examples are given to verify the developed approach and to demonstrate its practicality and effectiveness.

Sturm-Liouville Theory

Abstract: The chapter starts by considering ODEs subject to boundary conditions, and then considers the conditions under which the operator defining the ODE, together with the boundary conditions is Hermitian. This analysis, Sturm-Liouville theory, includes techniques for making an operator self-adjoint by multiplying its ODE by a weight factor and making an appropriate definition of the scalar product. The use of specific properties of ODEs to aid in the solution of boundary-value problems is illustrated for the Legendre and Hermite operators, and a two-region problem is used to illustrate the effect of matching conditions. The variation method (common in quantum mechanics) is described and illustrated.

Network operator requirements for the next generation of optical access networks

Abstract: This article describes FSAN operator perspectives on the drivers and system requirements for fiber access beyond 10-Gigabit-class PON systems (i.e., NG-PON2 in FSAN terminology). Additionally, a review of potential solutions in scope for NG-PON2 is given in the context of these operator drivers and requirements.

The induced generalized aggregation operators for intuitionistic fuzzy sets and their application in group decision making

Abstract: In this paper, we present the induced generalized intuitionistic fuzzy ordered weighted averaging (I-GIFOWA) operator. It is a new aggregation operator that generalized the IFOWA operator, including all the characteristics of both the generalized IFOWA and the induced IFOWA operators. It provides a very general formulation that includes as special cases a wide range of aggregation operators for intuitionistic fuzzy information, including all the particular cases of the I-IFOWA operator, GIFOWA operator and the induced intuitionistic fuzzy ordered geometric (I-IFOWG) operator. We also present the induced generalized interval-valued intuitionistic fuzzy ordered weighted averaging (I-GIIFOWA) operator to accommodate the environment in which the given arguments are interval-valued intuitionistic fuzzy sets. Further, we develop procedures to apply them to solve group multiple attribute decision making problems with intuitionistic fuzzy or interval-valued intuitionistic fuzzy information. Finally, we present their application to show the effectiveness of the developed methods.

A generalization of the power aggregation operators for linguistic environment and its application in group decision making

Abstract: We introduce a wide range of linguistic generalized power aggregation operators. First, we present the generalized power average (GPA) operator and the generalized power ordered weighted average (GPOWA) operator. Then we extend the GPA operator and the GPOWA operator to linguistic environment and propose the linguistic generalized power average (LGPA) operator, the weighted linguistic generalized power average (WLGPA) operator and the linguistic generalized power ordered weighted average (LGPOWA) operator, which are aggregation functions that use linguistic information and generalized mean in the power average (PA) operator. We give their particular cases such as the linguistic power ordered weighted average (LPOWA) operator, the linguistic power ordered weighted geometric average (LPOWGA) operator, the linguistic power ordered weighted harmonic average (LPOWHA) operator and the linguistic power ordered weighted quadratic average (LPOWQA) operator. Finally, we develop an application of the new approach in a multiple attribute group decision making problem concerning the evaluation of university faculty for tenure and promotion.

Quantum Simulation of Interacting Fermion Lattice Models in Trapped Ions

Abstract: IKERBASQUE, Basque Foundation for Science, Alameda Urquijo 36, 48011 Bilbao, Spain(Dated: November 28, 2011)We propose a method of simulating many-body interacting fermion lattice models in trapped ions,including highly nonlinear interactions in arbitrary spatial dimensions and for arbitrarily distantcouplings. We encode the products of fermionic operators in nonlocal spin operators of an ion string,which are eciently implementable, while a Trotter expansion of the total evolution operator canbe applied by using only polynomial resources. The proposed scheme can be relevant in a variety of elds as condensed-matter or high-energy physics, where quantum simulations may solve problemsintractable for classical computers.

On the Definitions of Nabla Fractional Operators

Abstract: We show that two recent definitions of discrete nabla fractional sum operators are related. Obtaining such a relation between two operators allows one to prove basic properties of the one operator by using the known properties of the other. We illustrate this idea with proving power rule and commutative property of discrete fractional sum operators. We also introduce and prove summation by parts formulas for the right and left fractional sum and difference operators, where we employ the Riemann-Liouville definition of the fractional difference. We formalize initial value problems for nonlinear fractional difference equations as an application of our findings. An alternative definition for the nabla right fractional difference operator is also introduced.

Color-kinematics duality and double-copy construction for amplitudes from higher-dimension operators

Abstract: We investigate color-kinematics duality for gauge-theory amplitudes produced by the pure nonabelian Yang-Mills action deformed by higher-dimension operators. For the operator denoted by F 3, the product of three field strengths, the existence of color-kinematic dual representations follows from string-theory monodromy relations. We provide explicit dual representations, and show how the double-copy construction of gravity amplitudes based on them is consistent with the Kawai-Lewellen-Tye relations. It leads to the amplitudes produced by Einstein gravity coupled to a dilaton field ϕ, and deformed by operators of the form ϕR 2 and R 3. For operators with higher dimensions than F 3, such as F 4-type operators appearing at the next order in the low-energy expansion of bosonic and superstring theory, the situation is more complex. The color structure of some of the F 4 operators is incompatible with a simple color-kinematics duality based on structure constants f abc, but even the color-compatible F 4 operators do not admit the duality. In contrast, the next term in the α′ expansion of the superstring effective action — a particular linear combination of D 2 F 4 and F 5-type operators — does admit the duality, at least for amplitudes with up to six external gluons.